An adult takes 400mg of ibuprofen. each hour, the amount of ibuprofen in the person's
system decreases by 29%. if 100mg of ibuprofen is left, how much time has passed? use
a = pert

4.048 hours

Step-by-step explanation:

A = Pe^(rt)

After 1 hour, the amount decreases by 29% (A = 0.71P), so r is:

0.71P = Pe^(r×1)

0.71 = e^r

r = ln(0.71)

r = -0.342

P = 400.  When A = 100, the time t is:

100 = 400e^(-0.342 t)

0.25 = e^(-0.342 t)

ln(0.25) = -0.342 t

t = -ln(0.25) / 0.342

t ≈ 4.048

Approximately 4.048 hours have passed.